### On the homology theory of categories. I.

Azmi Hanna (1971)

Journal für die reine und angewandte Mathematik

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Azmi Hanna (1971)

Journal für die reine und angewandte Mathematik

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Azmi Hanna (1972)

Journal für die reine und angewandte Mathematik

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S. K. Kaul (1970)

Colloquium Mathematicae

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Gudrun Kalmbach (1976)

Journal für die reine und angewandte Mathematik

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Marian Mrozek, Bogdan Batko (2010)

Annales Polonici Mathematici

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We generalize the notion of cubical homology to the class of locally compact representable sets in order to propose a new convenient method of reducing the complexity of a set while computing its homology.

Bruns, Winfried, Vetter, Udo (1998)

Beiträge zur Algebra und Geometrie

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Yu. T. Lisitsa, S. Mardešić (1986)

Banach Center Publications

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S. Dragotti, G. Magro, L. Parlato (2006)

Bollettino dell'Unione Matematica Italiana

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We give, here, a geometric treatment of intersection homology theory.

Daniel Krasner (2009)

Fundamenta Mathematicae

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We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl₃-homology.

Z. Fiedorowicz, T. Pirashvili (1995)

Mathematische Annalen

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A. Blanco, J. Majadas, A.G. Rodicio (1996)

Inventiones mathematicae

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Steven Garavaglia (1978)

Fundamenta Mathematicae

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L. Reid, S. Geller, C. Weibel (1989)

Journal für die reine und angewandte Mathematik

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Steven Boyer, Daniel Lines (1990)

Journal für die reine und angewandte Mathematik

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Gregory R. Conner, Samuel M. Corson (2016)

Fundamenta Mathematicae

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We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer...

Krzysztof K. Putyra (2014)

Banach Center Publications

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We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms along any 3-dimensional subcube is trivial. This allows us to create a chain complex whose homotopy type modulo certain relations is a link invariant. Both the original and...

L. D. Mdzinarishvili (1986)

Banach Center Publications

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